Definition of a Factor
A factor of a number is another number that divides it without leaving a remainder. In simple terms, a factor is a whole number that can be multiplied by another whole number to get the original number. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12. These numbers can divide 12 without leaving a remainder and can be multiplied together to equal 12.
Factors of 144
The factors of 144 are numbers that can divide 144 evenly without any remainder. These factors are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144. Factors are important in many mathematical operations such as simplifying expressions, finding the greatest common divisor, and solving equations.
Also Check: Factors of 12
Steps to Calculate the Prime Factors of 144
To find the prime factors of 144, follow these steps:
- Divide by the smallest prime number: Start with the smallest prime number that divides 144. Here, it is 2.
- Continue dividing by 2: Keep dividing the result by 2 until it is no longer divisible by 2.
- Move to the next smallest prime number: Once 2 is no longer a divisor, move to the next smallest prime number, which is 3, and repeat the process.
- Express the result: Write down the prime factorization by listing the prime numbers and their powers.
Prime Factorization of 144
Prime factorization breaks a number into its prime components. For 144, follow these steps:
- Divide 144 by 2: 144÷2=72
- Divide 72 by 2: 72÷2=36
- Divide 36 by 2: 36÷2=18
- Divide 18 by 2: 18÷2=9
- Divide 9 by 3: 9÷3=3
- Divide 3 by 3: 3÷3=1
So, the prime factors of 144 are 24×32 or 2×2×2×2×3×3
Example of Prime Factorization
- 144÷2=72
- 72÷2=36
- 36÷2=18
- 18÷2=9
- 9÷3=3
- 3÷3=1
Prime factors are 2×2×2×2×3×3
Importance of Factors and Prime Factorization
Factors and prime factorization are crucial in mathematics. They are used to:
- Find the greatest common divisor (GCD)
- Reduce fractions to their simplest form
- Solve mathematical equations
Understanding how to find factors and prime factors helps in simplifying complex mathematical problems and is a foundational skill in various areas of math.
Frequently Asked Questions
Factors are integers that can be divided evenly into another number. For instance, the factors of 18 include 1, 2, 3, 6, 9, and 18.
No, 144 is not a prime number. Prime numbers are positive integers that have no divisors other than 1 and themselves.
The number 144 has 14 factors in total.
The first ten multiples of 144 are as follows: 144 × 1 = 144, 144 × 2 = 288, 144 × 3 = 432, 144 × 4 = 576, 144 × 5 = 720, 144 × 6 = 864, 144 × 7 = 1008, 144 × 8 = 1152, 144 × 9 = 1296, and 144 × 10 = 1440.
The factors of 16 are 1, 2, 4, 8, and 16, while the factors of 144 are 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, and 144.